Periodic electric fields

Kabanov and Zingel [352] have recently published a comprehensive review of studies of the effect of application of continuous or periodic electric fields on the reactant during thermal decomposition of a solid. They comment on the superficiality of most of the work discussed. The application of an electric field is contrasted with the effect of selected additives as a means of obtaining information on the mechanism of a decomposition reaction. Both may alter the concentration of free electrons in the solid, but the effect of the field is more apparent in the vicinity of the surface. An example of an investigation of the effect of an electric field on a reaction is to be found in the work of the Panafieu et al. [373] on KN3. 

The same information may be obtained from purely rotational far infrared spectroscopy (FIR) and depolarized Rayleigh spectra. Dielectric relaxation measurements are also used for the same goal, most successfully in combination with far-infrared data. The absorption coefficient of a periodic electric field... 

Dielectric analysis (DEA) measures the electrical properties of a material as it is subjected to a periodic electric field under various conditions. This technique provides quantitative information on the capacitance and conductance of the ma-... 

Let us illustrate the simplest response approach by an example representing the many-particle system counterpart of Eqn. (5.1). Let F(t) stem from an (periodic) electric field E(t) acting upon an electric charge. The response of a dielectric with permittivity to the field E is the displacement... 

A. Barletta and E. Zanchini, Hyperbolic heat conduction and thermal resonances in a cylindrical solid carrying a steady-periodic electric field, Int. J. Heat Mass Transf. 39, 1307-1315 (1996). 

These examples are instructive, but it is important to note that experimentally we neither rely on a strictly periodic electric field nor on the assumption of a chirp free pulse train. The strict periodicity of the spectrum as stated in Eqn. 7 and the possibility to resolve single modes are the only requirements that enable the fs laser system to achieve precise optical to radio frequency conversions. 

To avoid computation of the periodic electric field arising from the (in any case artifidal) periodic boundary conditions, they coimt the interactions of each molecule with only those neighbours which lie within a sphere of radius about 9 A. ThQr show how to allow for this in order to estimate the Kirkwood static correlation factor g. . The factor involved is far from unity, being 9 o/[(co + 2)(2cq -b 1)] with Co 75, and it is not evident what (smaller) change will be needed in Nee and Zwanzig s analysis. 

These new molecular tensors seem very promising, as they are related to other spectroscopic parameters. A periodic magnetic field induces an electric field at the nuclei, which can be described in terms of an electromagnetic shielding tensor [15]. This is related to the intensity of absorption bands in vibrational circular dichroism (VCD) [16, 20]. Also, in the presence of a periodic electric field, the nuclei are acted upon by an induced magnetic field. This leads to the definition of magnetoelectric shielding [15]. 

Mollee, T.R. Anissimov, Y.G. Roberts, M.S. Periodic electric field enhanced transport through membranes. J. Membr. Sci. 2006, 278, 290-300. 

As discussed in Sect. 3.2, the internal periodic electric field described above will modulate the refractive index of an electro-optic material (see Eq. 37). The resulting index modulation can be written as... 

Athayde, A. L. "The Effects of Periodic Electric Fields on Carrier-Facilitated Membrane Transport" Ph.D. Thesis, University of Notre Dame, IN, 1985. 

E (cot) time-dependent periodic electric field (Chapter 7)... 

Robertson, B. Astumian, R. D. Tsong, T. Y. Nonlinear effects of periodic electric fields on membrane proteins. In Charge-Field Effects in Biosystems Allen, M. J., Ed. Plenum New York Vol. II, pp 191-209. 

In particular, by this approach, the kinetics of the electrons in moving and standing striations, occurring at low discharge currents in dc column plasmas, can be investigated (Sigeneger e/ al., 1998). Under the action of the highly modulated, spatially periodic electric field of the striations, an undamped, spatially periodic evolution of all electron kinetic properties is established. 

The fascinating phenomenon of surface plasmon resonance (SPR) occurs when an electromagnetic wave interacts with the conduction electrons of a metal (6). The periodic electric field of the electromagnetic wave causes a collective oscillation of the conductance electrons at a resonant frequency relative to the lattice of positive ions. Light is absorbed or scattered at this resonant frequency. The process of... 

A classical paper on molecules in a static or periodic electric field. 

EA spectroscopy measures the normalized variation of the transmission of light through a sample (conjugated polymer films in this study) upon application of a periodic electric field [85,86]. 

This technique is used principally for the rheological characterisation of polymers and measurement of the dielectric constant. The technique measures changes in the properties of a polymer as it is subjected to a periodic electric field. This produces quantitative data, which can be used to determine the capacitive and conductive nature of a material. Molecular relaxations can be characterised and flow and cure of resins can be monitored. 

However, the effects of single and periodical electric field pulses on cell - as well as magnetic influences on tissues - have been studied intensively only recently, because of its importance for good engineering, biotechnology, and medicine. The reason this this, are the new possibilities of pulses causing ... 

Let us consider the wave vectors K from the vicinity of the first Brillouin zone origin (i.e. K 0). It corresponds to the infrared active lattice vibrations with X > > a. The optical phonon branch has the highest vibration frequency possible for the atom chain in that case. The ions vibrate with the opposite phases and amplitudes inversely proportional to their masses. Dipole moments are effectively created in each elementary unit and therefore the crystal is polarized. Polarization of the crystal causes the internal periodical electric field E at the position of each atom. This field contributes to the additional electric force on each ion, either by - -eEi, or by —eE force. Let us further denote the stiffness of the nearest neighbor interaction (i.e. spring constant) by C and displacement of ions A and B by w.4, ub respectively. The ion displacements follow the differential equation of motion... 

Consider a molecular system described by the Hamiltonian operator Ho(r,R) where r and R are vectors containing the electronic and nuclear coordinates, respectively. This Hamiltonian acts in the Hilbert space H spanned by the basis of eigenstates of Ho. The dynamics of the system in interaction with a periodic electric field e(0 = ocos(a f - - 0) with eq = eoe in the semiclassical dipole approximation is described by the TDSE... 

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